Existence of positive ground state solutions for the coupled Choquard system with potential

Jianqing Chen and Qian Zhang

Mathematische Nachrichten, 2023, vol. 296, issue 9, 4043-4059

Abstract: In this paper, we study the following coupled Choquard system in RN$\mathbb {R}^N$: −Δu+A(x)u=2pp+qIα*|v|q|u|p−2u,−Δv+B(x)v=2qp+qIα*|u|p|v|q−2v,u(x)→0andv(x)→0as|x|→∞,$$\begin{align*} \hspace*{6pc}\left\lbrace \def\eqcellsep{&}\begin{array}{l} -\Delta u+A(x)u=\frac{2p}{p+q} {\left(I_\alpha \ast |v|^q\right)}|u|^{p-2}u,\\[3pt] -\Delta v+B(x)v=\frac{2q}{p+q}{\left(I_\alpha \ast |u|^p\right)}|v|^{q-2}v,\\[3pt] u(x)\rightarrow 0\ \ \hbox{and}\ \ v(x)\rightarrow 0\ \ \hbox{as}\ |x|\rightarrow \infty , \end{array} \right.\hspace*{-6pc} \end{align*}$$where α∈(0,N)$\alpha \in (0,N)$ and N+αN

Date: 2023
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